Rademacher formula

[Janitor]

Can anyone sketch out how Rademacher wound up with his formula for the number of ways to partition an integer? Or at least explain why the number 24 shows up in it?

(In the graphic link below, the A coefficients are themselves defined as a certain rather complicated sum of exponentials to the base e.)

[NateTG]

I don't really know anything about this, but
http://mathworld.wolfram.com/PartitionFunctionP.html

Indicates that Rademacher used farey sequences and ford circles

I'm guessing you've already been there though.

[Janitor]

Yes, Nate. In fact I grabbed the formula image file from that very page that you linked. I first came upon the formula in a layman's book on number theory by John Conway, but that book didn't offer a derivation if I recall.

[Sariaht]

Reminds of the solution to the third degree equation!

[Janitor]

Bumping this up in case some of the newer members can provide some insight.